At the two shows I've gone to (Chicago, both 2008 and 2010), I tried my damnedest to meet the band, or just any of them.
Both shows I actually managed to find and talk to the head of security, and begged them both times if we could meet any of the band members. They told me no, and so I asked him about the possibility of it after the show, and I was told both times that "The band will already be long gone before the lights even come on in the stadium".
The best advice I can give is (you will need to know the outline of the venue most likely) try and be there as they arrive/leave. Most areas probably even have this area closed off, but you never know when they might possibly pop out in sight. Also, keep in mind the airports as well, you could always try and catch them there (you'd probably have a much better chance as they land, instead of leaving, since they will obviously be in a hurry most likely).
I would give nothing more than to be able to meet Bruce Dickinson and just shake his hand. I wouldn't even need an autograph... hopefully I will finally be able to sometime in the future?